Question

Platinum has a face-centered cubic crystal structure and a density of 21.5 g/cm^3. What is the radius of a platinum atom?

Answer 1

Platinum has a face-centered cubic crystal structure and a density of 21.5 g/cm^3. The radius of the platinum atom is 139pm.

The radius of the platinum atom can be found by the relation of density and radius of atom.

Platinum has a face-centered cubic (fcc) crystal structure which means that 4 atoms are present in each structure.

Hence no. of atoms, Z=4

The radius of atom can be found out by substitution in the below formula:

Relation of density and radius of atom:

Density, d = Z × M / Nₐ × a³    

∴ where, Z is the no. of atoms = 4                

M is the Molecular mass of platinum = 195 g/mol    

 N is the Avogadro's number = 6 × 10²³ / mol                

 a is the radius of the atom = ?                

d is the density = 21.5 g/cm³

⇒ a³ = Z × M / Nₐ × d

⇒ a³ = 4 × 195 / 6 × 10²³ ×  21.5

⇒ a = 139 × 10⁻¹²m

a = 139pm

Hence, the radius of the platinum atom is 139pm.

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Answer 2

The answer is 139pm

The relationship between density and radius of an atom may be used to calculate the radius of a platinum atom.

Platinum has a face-centred cubic (fcc) crystal structure, which implies that each structure has four atoms.

As a result, the number of atoms is Z=4.

Substitution in the following formula yields the radius of an atom:

Atomic density and radius relationship:

Density,$d=Z \times M / N_{a} \times a^{3}$

$\therefore$ where, Z is the no. of atoms =4

$\mathrm{M}$ is the Molecular mass of platinum $=195 \mathrm{~g} / \mathrm{mol}$

$\mathrm{N}$is the Avogadro's number $=6 \times 10^{23} / \mathrm{mol}$

a is the radius of the atom = ?

$\mathrm{d}$ is the density $=21.5 \mathrm{~g} / \mathrm{cm}^{3}$

$\begin{aligned}&\Rightarrow a^{3}=Z \times M / N_{a} \times d \\&\Rightarrow a^{3}=4 \times 195 / 6 \times 10^{23} \times 21.5 \\&\Rightarrow a=139 \times 10^{-12} m \\&a=139 p m\end{aligned}$

What is platinum atom?

• Platinum is a periodic table element with the atomic number 78 and the atomic mass 195. It is a very uncommon element found in the earth's crust.
• Because of its grey-white silvery color, the name platinum is derived from Platina (Spanish for "small silver").

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